{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J5JSTWQPPLF6WSUHOGASCWCSQU","short_pith_number":"pith:J5JSTWQP","canonical_record":{"source":{"id":"1404.1149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-04T03:59:58Z","cross_cats_sorted":[],"title_canon_sha256":"2ad164238eb3c6e224d407d5c935ee4006fe7d6fedaf54c62e857c9a9efc5aa9","abstract_canon_sha256":"d17ac58bf2cf78738607cc4bdb160b72bbf18deb7c191fa7fb3a021c010305a4"},"schema_version":"1.0"},"canonical_sha256":"4f5329da0f7acbeb4a8771812158528528c0f355afeae969c396009e08c04b75","source":{"kind":"arxiv","id":"1404.1149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1149","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1149v2","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1149","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"J5JSTWQPPLF6","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J5JSTWQPPLF6WSUH","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J5JSTWQP","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J5JSTWQPPLF6WSUHOGASCWCSQU","target":"record","payload":{"canonical_record":{"source":{"id":"1404.1149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-04T03:59:58Z","cross_cats_sorted":[],"title_canon_sha256":"2ad164238eb3c6e224d407d5c935ee4006fe7d6fedaf54c62e857c9a9efc5aa9","abstract_canon_sha256":"d17ac58bf2cf78738607cc4bdb160b72bbf18deb7c191fa7fb3a021c010305a4"},"schema_version":"1.0"},"canonical_sha256":"4f5329da0f7acbeb4a8771812158528528c0f355afeae969c396009e08c04b75","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:51.496984Z","signature_b64":"OxAh2SAegSnNP0Xy9xmr5u/d9hrPU8QncXsffG85ikI9JqXAShPDUD791A6gIKZwiLJM2obkql4E4pGc7wbtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f5329da0f7acbeb4a8771812158528528c0f355afeae969c396009e08c04b75","last_reissued_at":"2026-05-18T00:32:51.496366Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:51.496366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.1149","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NsgBSLpB0WZMXYPQaE6lVqrg41jZuI5cpECxTOsJD0Y8K6cLIn+J1x6hHwpZWNrCxqlbvGAsKHosOKjBhe1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:26:38.688997Z"},"content_sha256":"10d5d4bc874c9b39a28b3a4010a488062378e6a2f4bf29a0d1ba060add1a616b","schema_version":"1.0","event_id":"sha256:10d5d4bc874c9b39a28b3a4010a488062378e6a2f4bf29a0d1ba060add1a616b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J5JSTWQPPLF6WSUHOGASCWCSQU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generic property and conjugacy classes of homogeneous Borel subalgebras of restricted Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Bin Shu","submitted_at":"2014-04-04T03:59:58Z","abstract_excerpt":"Let $(\\mathfrak{g},[p])$ be a finite-dimensional restricted Lie algebra over an algebraically closed field $\\mathbb{K}$ of characteristic $p>0$, and $G$ be the adjoint group of $\\mathfrak{g}$. We say that $\\mathfrak{g}$ satisfying the {\\sl generic property} if $\\mathfrak{g}$ admits generic tori introduced in \\cite{BFS}. A Borel subalgebra (or Borel for short) of $\\mathfrak{g}$ is by definition a maximal solvable subalgebra containing a maximal torus of $\\mathfrak{g}$, which is further called generic if additionally containing a generic torus. In this paper, we first settle a conjecture propose"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1149","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IoVQT1mSLR6HLa+MzDr5vkIt9ZbQPfWteYCP3nbadSFyV00aRsMMPOw1m/EXam/32/0o3ua4WFUFzPF2oGvpDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:26:38.689777Z"},"content_sha256":"2579cfccf3b9f12cc9e5001a1bbe1f0bc3175ffee2a84ee144f8e5e27495aeb8","schema_version":"1.0","event_id":"sha256:2579cfccf3b9f12cc9e5001a1bbe1f0bc3175ffee2a84ee144f8e5e27495aeb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J5JSTWQPPLF6WSUHOGASCWCSQU/bundle.json","state_url":"https://pith.science/pith/J5JSTWQPPLF6WSUHOGASCWCSQU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J5JSTWQPPLF6WSUHOGASCWCSQU/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T22:26:38Z","links":{"resolver":"https://pith.science/pith/J5JSTWQPPLF6WSUHOGASCWCSQU","bundle":"https://pith.science/pith/J5JSTWQPPLF6WSUHOGASCWCSQU/bundle.json","state":"https://pith.science/pith/J5JSTWQPPLF6WSUHOGASCWCSQU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J5JSTWQPPLF6WSUHOGASCWCSQU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J5JSTWQPPLF6WSUHOGASCWCSQU","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"d17ac58bf2cf78738607cc4bdb160b72bbf18deb7c191fa7fb3a021c010305a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-04T03:59:58Z","title_canon_sha256":"2ad164238eb3c6e224d407d5c935ee4006fe7d6fedaf54c62e857c9a9efc5aa9"},"schema_version":"1.0","source":{"id":"1404.1149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.1149","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"arxiv_version","alias_value":"1404.1149v2","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1149","created_at":"2026-05-18T00:32:51Z"},{"alias_kind":"pith_short_12","alias_value":"J5JSTWQPPLF6","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J5JSTWQPPLF6WSUH","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J5JSTWQP","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:2579cfccf3b9f12cc9e5001a1bbe1f0bc3175ffee2a84ee144f8e5e27495aeb8","target":"graph","created_at":"2026-05-18T00:32:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $(\\mathfrak{g},[p])$ be a finite-dimensional restricted Lie algebra over an algebraically closed field $\\mathbb{K}$ of characteristic $p>0$, and $G$ be the adjoint group of $\\mathfrak{g}$. We say that $\\mathfrak{g}$ satisfying the {\\sl generic property} if $\\mathfrak{g}$ admits generic tori introduced in \\cite{BFS}. A Borel subalgebra (or Borel for short) of $\\mathfrak{g}$ is by definition a maximal solvable subalgebra containing a maximal torus of $\\mathfrak{g}$, which is further called generic if additionally containing a generic torus. In this paper, we first settle a conjecture propose","authors_text":"Bin Shu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-04T03:59:58Z","title":"Generic property and conjugacy classes of homogeneous Borel subalgebras of restricted Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1149","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:10d5d4bc874c9b39a28b3a4010a488062378e6a2f4bf29a0d1ba060add1a616b","target":"record","created_at":"2026-05-18T00:32:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"d17ac58bf2cf78738607cc4bdb160b72bbf18deb7c191fa7fb3a021c010305a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2014-04-04T03:59:58Z","title_canon_sha256":"2ad164238eb3c6e224d407d5c935ee4006fe7d6fedaf54c62e857c9a9efc5aa9"},"schema_version":"1.0","source":{"id":"1404.1149","kind":"arxiv","version":2}},"canonical_sha256":"4f5329da0f7acbeb4a8771812158528528c0f355afeae969c396009e08c04b75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f5329da0f7acbeb4a8771812158528528c0f355afeae969c396009e08c04b75","first_computed_at":"2026-05-18T00:32:51.496366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:51.496366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OxAh2SAegSnNP0Xy9xmr5u/d9hrPU8QncXsffG85ikI9JqXAShPDUD791A6gIKZwiLJM2obkql4E4pGc7wbtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:51.496984Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.1149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10d5d4bc874c9b39a28b3a4010a488062378e6a2f4bf29a0d1ba060add1a616b","sha256:2579cfccf3b9f12cc9e5001a1bbe1f0bc3175ffee2a84ee144f8e5e27495aeb8"],"state_sha256":"3cf35bc7b7ba2f616cbf0961f5dcb614030465545fb22841999128882121a19c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eRxLL9IBr+fimI24idNDLi2xRSqn9Da6FsTpZ9HwOA+Mo77le9EVGoX1tnptrDGbIi3Hp9BEXHYRuFUaabkBBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:26:38.694019Z","bundle_sha256":"9a63d20780709e257a15812fa1d29fe11392768f30f8e29a4df0a83fcc223e3c"}}